236,948 research outputs found
The Operator form of 3H (3He) and its Spin Structure
An operator form of the 3N bound state is proposed. It consists of eight
operators formed out of scalar products in relative momentum and spin vectors,
which are applied on a pure 3N spin 1/2 state. Each of the operators is
associated with a scalar function depending only on the magnitudes of the two
relative momenta and the angle between them. The connection between the
standard partial wave decomposition of the 3N bound state and the operator form
is established, and the decomposition of these scalar function in terms of
partial wave components and analytically known auxiliary functions is given.
That newly established operator form of the 3N bound state exhibits the
dominant angular and spin dependence analytically. The scalar functions are
tabulated and can be downloaded. As an application the spin dependent nucleon
momentum distribution in a polarized 3N bound state is calculated to illustrate
the use of the new form of the 3N bound state.Comment: 21 pages, 1 table, 8 figures, revtex
A New Perspective on Path Integral Quantum Mechanics in Curved Space-Time
A fundamentally different approach to path integral quantum mechanics in
curved space-time is presented, as compared to the standard approaches
currently available in the literature. Within the context of scalar particle
propagation in a locally curved background, such as described by Fermi or
Riemann normal co-ordinates, this approach requires use of a constructed
operator to rotate the initial, intermediate, and final position ket vectors
onto their respective local tangent spaces, defined at each local time step
along some arbitrary classical reference worldline. Local time translation is
described using a quantum mechanical representation of Lie transport, that
while strictly non-unitary in operator form, nevertheless correctly recovers
the free-particle Lagrangian in curved space-time, along with new
contributions. This propagator yields the prediction that all probability
violating terms due to curvature contribute to a quantum violation of the weak
equivalence principle, while the remaining terms that conserve probability also
correspondingly satisfy the weak equivalence principle, at least to
leading-order in the particle's Compton wavelength. Furthermore, this
propagator possesses an overall curvature-dependent and gauge-invariant phase
factor that can be interpreted as the gravitational Aharonov-Bohm effect and
Berry's phase.Comment: 14 pages, 1 figure; major additions and revisions introduced; main
conclusions are unchanged; new affiliation adde
Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions
We describe how the semiclassical theory of radical pair recombination
reactions recently introduced by two of us [D. E. Manolopoulos and P. J. Hore,
J. Chem. Phys. 139, 124106 (2013)] can be generalised to allow for different
singlet and triplet recombination rates. This is a non-trivial generalisation
because when the recombination rates are different the recombination process is
dynamically coupled to the coherent electron spin dynamics of the radical pair.
Furthermore, because the recombination operator is a two-electron operator, it
is no longer sufficient simply to consider the two electrons as classical
vectors: one has to consider the complete set of 16 two-electron spin operators
as independent classical variables. The resulting semiclassical theory is first
validated by comparison with exact quantum mechanical results for a model
radical pair containing 12 nuclear spins. It is then used to shed light on the
spin dynamics of a carotenoid-porphyrin-fullerene (CPF) triad containing
considerably more nuclear spins which has recently been used to establish a
'proof of principle' for the operation of a chemical compass [K. Maeda et al.,
Nature 453, 387 (2008)]. We find in particular that the intriguing biphasic
behaviour that has been observed in the effect of an Earth-strength magnetic
field on the time-dependent survival probability of the photo-excited C+PF-
radical pair arises from a delicate balance between its asymmetric
recombination and the relaxation of the electron spin in the carotenoid
radical
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